3. (5/15) Consider an autoregressive model |ρΊκ 1. Is E (utlXt, X1-1, )-0? w here ut is Γ.Γ.d with mean 0 and variance ge and 3. (5/15) Consider an autoregressive model |ρΊκ 1. Is E (utlXt, X1-1...
1. Consider the following autoregressive process 2+ = 4.0 + 0.8 2t-1 + Ut, where E (u+12+-1, Zt-2, ....) = 0 and Var (ut|2t-1, 2-2, ...) = 0.3. The unconditional E (Zt) and unconditional variance Var (zt) are: (a) E (2+) = 11.1111, Var (zł) = 0.8333 (b) E (2+) = 11.1111, Var (zt) = 1.5 (c) E (zt) = 20, Var (zt) = 0.8333 (d) E (2+) = 4, Var (zł) = 0.8333 (e) E (Zt) = 4,Var (z+)...
please solve this problems
Consider the following autoregressive processes: W 2W-1X Wo 0 Zn = 3/4 Zq-1 + Xn Zo = 0. (a) Suppose that Xn is a Bernoulli process. What trends do the processes exhibit? (b) Express Wn and Zn in terms of Xn, Xn-1, ..., X1 and then find E[Wn] and E[Zn]. Do these results agree with the trends you expect? (c) Do Wn or Zn have independent increments? stationary increments? (d) Generate 100 outcomes of a Bernoulli...
Consider the following AR(1) model: 1. a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. the following random 2. Consider walk model: yeBo yt-1 +ut, t-0,1,..,T a. Show that yt-3βο + yt-3 + ut + ut-1 + ut-2. b. Suppose that 0-0, show that y.-t βο +4 + ut-1 + + u! c. Suppose that that yo -0, and ut for all t are ii.d. with mean 0 and variance...
Consider the following
model
1. Consider the following AR(1) model: a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. b. Show that 1 t-2 2. Consider the following random walk model: ytBo yt-1 +ut, t 0,1,...,T Show that ye 3o yt-3 + ut + Ut-1 +t-2 Suppose that yo - 0, show that yt - tPo + ut + ut-1++u, Suppose that that yo -0, and ut for all t...
Consider a population linear regression model: Yt=β0 + β1Xt + ut Calculate: 1. Variance 2. Covariance of ut and Xt 3. β0 4. β1
Consider the 5 point running mean where ut ~ NID(0, σ ), and let σ -1. (i) Determine the theoretical auto-covariance (ACF) for v, and the theoretical cross-covariance function (CCF) between w and vt. (ii) Generate a realization of w of length 1000, compute the associated 5-point moving average v and plot these two time series on the same graph.i Calculate the corresponding sample versions for the ACF and CCF and remark on how these resemble and differ from the...
1. Suppose that X1, X2, and X3 E(X1) = 0, E(X2) = 1, E(X3) = 1, Var(X1) = 1, Var(X2) = 2, Var(X3) = 3, Cov(X1, X2) = -1, Cov(X2, X3) = 1, where X1 and X3 are independent. a.) Find the covariance cov(X1 + X2, X1 - X3). b.) Define U = 2X1 - X2 + X3. Find the mean and variance of U.
Consider the model, Yt = 0.8 + 0.1 Yt-1 +0.5 X1,t + 1.7 X2,t + Ut. Complete the following table for the predicted values (2 decimals): 2018 2019 2020 2021 Year Yt 7.1 7.63 1.25 1.35 X1,5 KX2,0 1.30 1.9 1.40 2.4 2.5 3.20
Consider the model, Yt = BO + p1 Yt-1 + Ut, select the assumption(s) that are needed to prove unbiased parameter estimates. (A. E[Ut Us |X, Yt-1, Yt-2, ... ] = 0 B. |p1|< 1 C. E[ Ut? |X, Yt-1, Yt-2, ... ] = su? D. E[ Ut |X, Yt-1, Yt-2, ... ] = 0
Consider the following point estimators, W, X, Y, and Z of μ: W = (x1 + x2)/2; X = (2x1 + x2)/3; Y = (x1 + 3x2)/4; and Z = (2x1 + 3x2)/5. Assuming that x1 and x2 have both been drawn independently from a population with mean μ and variance σ2 then which of the following is true... Which of the following point estimators is the most efficient? A. X B. W C. Y D. Z